Study of the Effects of Remote Heavy Group Vibrations on the Temperature Dependence of Hydride Kinetic Isotope Effects of the NADH/NAD+ Model Reactions

It has recently been observed that the temperature(T)-dependence of KIEs in H-tunneling reactions, characterized by isotopic activation energy difference (ΔEa = EaD – EaH), is correlated to the rigidity of the tunneling ready states (TRSs) in enzymes. A more rigid system with narrowly distributed H-donor–acceptor distances (DADs) at the TRSs gives rise to a weaker T-dependence of KIEs (i.e., a smaller ΔEa). Theoreticians have attempted to develop new H-tunneling models to explain this, but none has been universally accepted. In order to further understand the observations in enzymes and provide useful data to build new theoretical models, we have studied the electronic and solvent effects on ΔEa’s for the hydride-tunneling reactions of NADH/NAD+ analogues. We found that a tighter charge-transfer (CT) complex system gives rises to a smaller ΔEa, consistent with the enzyme observations. In this paper, we use the remote heavy group (R) vibrational effects to mediate the system rigidity to study the rigidity−ΔEa relationship. The specific hypothesis is that slower vibrations of a heavier remote group would broaden the DAD distributions and increase the ΔEa value. Four NADH/NAD+ systems were studied in acetonitrile but most of such heavy group vibrations do not appear to significantly increase the ΔEa. The remote heavy group vibrations in these systems may have not affected the CT complexation rigidity to a degree that can significantly increase the DADs, and further, the ΔEa values.


■ INTRODUCTION
Kinetic isotope effect (KIE) and its temperature (T) dependence are important tools to study the hydrogen(H)transfer reaction mechanisms.Semiclassically, the primary deuterium (D) KIE is smaller than 7, and the isotopic activation energy difference (ΔE a = E aD − E aH ), which reflects the T-dependence of KIEs, is between 1.0 and 1.2 kcal/mol. 1hen KIEs are outside of the limits, a quantum H-tunneling mechanism is suggested, but discussion of the nature of the tunneling including the structure of the corresponding transition state (TS), i.e., the tunneling-ready state (TRS), has seldom been mentioned. 1Traditional Bell tunneling model does not provide any prediction about the relationship between structure and tunneling probability and cannot explain all of the KIE results.−14 These latter tunneling models provide a possibility to understand the relationship between structure and tunneling mechanisms.
One full tunneling model is the vibration-assisted activated H-tunneling (VA-AHT) model. 10,12,13This model contains two orthogonal activation processes, in one process, thermal heavy atom motions (vibrations) bring a H-donor (Don-H) and -acceptor (Acc) to the activated TRS ([Don-H---H-Acc] ‡ ) that has degenerate reactant [Don-H] ‡ and product [H-Acc] ‡ states for H-tunneling ready to occur at a ground state level, and in the other process, the motions sample the shorter donor−acceptor distances (DADs) allowing effective tunneling to happen.(In the TRS, H is at both the donor and acceptor at the same time, being in a quantum state.)Since the first activation process is H-isotope insensitive and the D-tunneling requires shorter DADs due to the shorter wavelength of D vibrations, ΔE a results from the second DAD sampling activation process and E aD is larger than E aH (ΔE a > 0).When the system is rigid enough to make the DAD sampling impossible, E aD is equal to E aH making ΔE a = 0. Therefore, a more rigid system gives rise to a smaller ΔE a .This model predicts a relationship between structure and ΔE a magnitudes.
−17 Test of the model can use the study of the system rigidity−ΔE a relationship.Study of the latter relation-ship could also provide information to help build future necessary H-transfer/tunneling models.A highly rigid system represents a system of densely populated DADs which could be sampled by strong heavy atom vibrations on the DAD sampling coordinate.The rigidity/DAD−ΔE a relationship has been studied for H-transfer reactions in enzymes and solution.8][29][30]32 Results have been used to provide insight into how protein dynamics modulate the short and thus narrowly distributed DADs in enzyme catalysis.
−39 In our studies, we use structural and solvent effects to modulate the rigidity of the systems and correlate the DAD information with the observed ΔE a 's.We use the hydride transfer reactions of NADH/NAD + analogues for the study.One reason to use these reactions is that the hydride transfer takes place in a π−π charge-transfer (CT) complex so that the system rigidity design could use the electronic and steric considerations.Another reason is that the current rigidity/DAD−ΔE a relationship study for hydride transfer enzymes only involve NADH/NAD + coenzymes, so that our study can provide useful insight into the explanation of the observations in the corresponding enzymes.We found that a large difference in ΔE a comes from systems of very different hydride donating or accepting abilities that give significantly different tightness of the CT complexations and/or from systems of very different donor/acceptor structures that have interactions at various sites leading to different numbers of TRS complexes and thus very different DAD populations.
Another factor that potentially affects the system rigidity and can be used for our study may be the motions/vibrations of the remote heavy groups that have the same electronic properties and same steric effects.−42 This has been explained in terms of the slower local vibrations of proteins that lead to broadly distributed DADs.Here, we hypothesize that heavier remote group vibrations would slow down the CT complexation vibrations resulting in wider DAD populations and a larger ΔE a .We use four NADH/NAD + systems with remote heavy groups (R) designed to investigate the specific hypothesis.These include hydride transfers from 10-εalkylated (R) acridines (R−AH, R = methyl, n-propyl, and benzyl) to the 9-phenylxanthylium ion (PhXn + BF 4 − ) (System 1), from Hantzsch ester (HEH) to the oxidized forms of the R−AH's, i.e., 10-ε-alkylated acridinium ions (R−A + BF 4 − , plus R = n-hexyl) (System 2), from isopropanol and its βdeuterated and β-alkylated analogues (R = cyclohexyl (c-HexOH), n-propyl (4-HepOH)) to PhXn + BF 4 − (System 3), and from 2-phenyl-1,3-dimethylbenzimidazole (DMPBIH) to the R−A + BF 4 − (System 4).The T-dependence of KIEs of the reactions in acetonitrile were determined.The effects of the remote heavy group vibrations on ΔE a 's as well as the feasibility of the system design are discussed.It was found that most of these remote groups do not significantly affect the ΔE a 's, being outside of our expectations.Main factors that affect the ΔE a values in these and previously published systems are discussed.

■ RESULTS AND DISCUSSION
−45 We call these complexes as productive reactant complexes (PRCs).We have reported the spectroscopy evidence for the CT complex formation in the similar reactions. 34,46The PRCs are believed to form in a diffusioncontrolled rate.Theoretically, the hydride-transfer could be classical through a transition state (TS) or nonclassical through a TRS.This mechanism is described in eq 5. 37 The observed KIEs are derived from the second-order rate constants (k 2 ).They are related to the hydride transfer step (k H ), i.e., KIE = Perhaps, the best R group to use for study of the vibrational effects on the DAD sampling would be at an indirect remote reaction center whose hybridization also changes during the reaction and whose vibrations thus likely accompany with vibrations of the direct reaction centers.In the R−AH and R− A + , the 10-δ-R groups are at such a N reaction center whose hybridization changes in between sp 2 and sp 3 (for systems (1), (2), and (4)) so their vibrations would be expected to affect the DAD sampling.In the β-substituted isopropanol (RCH 2 CH(OH)CH 2 R) systems (3), our study looks into the effects of vibrations of the whole RCH 2 groups.To study the vibrational effects of the R groups only, the R must at first have very similar, if not the same, electronic effects.Indeed, the R groups we use in this paper have the similar substituent constants: CH 3 (σ = −0.17),n-C 3 H 7 (σ = −0.13),n-C 6 H 13 (σ = ∼ −0.16), and CH 2 Ph (σ = −0.09),basically satisfying the similar electronic property requirement.Another prerequisite for the study is their minimal steric interactions with the other reactant so that the system flexibility or DAD sampling would not be affected.While all of the R groups are remote from the reaction center so the minimal steric effect requirement is expected to be met, the steric effect is a complex factor that we will discuss for the individual system subsequently.
The representative second-order rate constants (k 2 ) and KIEs at 25 °C, the enthalpies (ΔH ‡ ) and entropies (ΔS ‡ ) of activation, as well as the ΔE a 's of the reactions are listed in Table 1.According to the reported hydride affinities of the PhXn + (−ΔG H − = 91.6 kcal/mol), MA + (76.2),HE + (64.4),DMPBI + (49.2) in acetonitrile, 47 the corresponding reactions are largely exothermic.For example, ΔG°= −15.4 kcal/mol for reaction (1) (R = Me), −11.8 kcal/mol for reaction (2) (R = Me), and −27.0 kcal/mol for reaction (4) (R = Me).We did not find the corresponding hydride affinity values of the oxidized forms of the alcohols, but we calculated the ΔG°= −4.6 kcal/mol for the hydride-transfer reaction (3) (R = H for isopropanol) in acetonitrile.The latter results indicate that the hydride transfer step of system (4) reactions is the least exothermic, making the reactions the slowest with highest enthalpies of activation among the four series of reactions.All of the entropies of activation are large negative values conforming to the fact that the bimolecular hydride transfer takes place in the tight CT complexes.
Like other hydride transfer reactions of NADH/NAD + models, these reactions have small KIEs (<7).The ΔE a 's are from ∼ 0−1.11 kcal/mol, some of which are within and some of which are outside of the semiclassical range of 1.0−1.2kcal/ mol.3][34][35]46,48 Furthermore, it has been shown that small KIEs from such hydride transfer reactions also fit to the Marcus theory of atom transfer that involves a H-tunneling component. 2,4,5In the meantime, the small KIE's and similar ΔE a values were also found in the hydride transfer reactions of NADH/NAD + in enzymes and mutants.11,13,25,26,28,49,50 As described in the Introduction, the latter observations have been explained following contemporary H-tunneling models.
The Remote ε-R Group Effects on ΔE a in Systems (1) and (2) Reactions.The ultimate goal of the work is to correlate the system rigidity with ΔE a .The overall hypothesis of our group study is that a more rigid system gives rise to a smaller ΔE a value.The specific hypothesis in this paper is that slower vibrations of a heavier remote group increase the DAD sampling range and thus the ΔE a value.Table 1 shows, however, that the change of R groups does not significantly change the ΔE a in most of the systems.The ΔE a 's are in the range from 0.88 to 0.94 kcal/mol for the reactions between R−AH and PhXn + (System 1), and in the range from 0.95 to 1.20 kcal/ mol for the reactions between RA + and HEH (System 2).A positive observation in these two systems ((1) and ( 2)) is that none of the ΔE a values are smaller than those for the reactions with the lightest remote CH 3 group (MAH and MA + ), but use of the relatively small ΔE a differences between reactions of different remote R groups to support our specific hypothesis in this paper may be reluctant.An interesting observation is, however, that the reactions of PAH and PA + (R = n-C 3 H 7 ) with the corresponding acceptor (PhXn + ) and donor (HEH) have consistently relatively larger ΔE a than those with MAH and MA + (R = CH 3 ).Using the reactions of these four compounds (PAH vs MAH, and PA + vs MA + ) with other hydride acceptors/donors to investigate the specific hypothesis in this paper is currently in progress to attempt to find whether the trend found is consistent throughout a large range of the reactions.
The Remote β-R Group Effects on ΔE a in System (3) Reactions.The remote R group effects on ΔE a 's for the System (3) reactions are largely the same as those for the systems ( 1) and ( 2), i.e., less significant effects were observed.
The ΔE a values have much larger deviations (different ways to determine the slow kinetics from others, see the Experimental and Computations section).This system does not have a π−π but an n−π complexation between alcohol O and the PhXn + ring, according to our previous report, so that the complexation vibrations could also affect the DAD sampling. 51,52Note that we have reported the ΔE a value (1.01 ± 0.26 kcal/mol) for the reaction of primary benzyl alcohol with PhXn + in acetonitrile. 33It is close to the ΔE a values of the reactions of the secondary alcohols in Table 1 (mostly 0.8 − 0.9 kcal/mol), further indicating that the alcohol group effect on the ΔE a 's of the class of reactions is small.Herein, change of the two CH 3 groups in isopropanol to two heavier CD 3 groups of the same electronic and steric effects (entries 8 vs 9 in Table 1) increases their mass by 20% but the ΔE a has almost no change.Note that we are aware that the β,β-2CH 3 /2CD 3 secondary (2°) KIE may affect the T-dependence of observed 1°KIEs, but it is very small, which is 1.05 at 25 °C, as we reported. 51,53herefore, T-dependence of such small 2°KIEs would not significantly affect the ΔE a value.The observed same ΔE a values from the two reactions suggest that the slower CD 3 vibrations do not appear to broaden the DAD populations in the reaction of isopropanol.
To compare the vibrational effects of the β-R groups in isopropanol (R = H) vs cyclohexanol (R = −CH 2 −CH 2 − CH 2 −) on ΔE a values (entries 8 vs 10), their steric effect difference should be discussed as they are relatively closer to the reaction center as compared to the ε-R group effects in systems ( 1) and ( 2).From both the classical TS and nonclassical TRS structures of the isopropanol reaction we reported, the 9-phenyl group of the PhXn + is far from the two alcohol methyl groups due to the restricted geometry of the T(R)S in which the transferring hydride points toward the 9-C of the PhXn + and the alcohol O complexes with the central ring of the same (also cf. the subsequent Figure 1 (A)). 51,52,54ange of the two methyl groups in isopropanol to the cyclic hexyl group in cyclohexanol would be expected to make the steric effect little changed.To confirm the latter, we calculated the classical TS structures for both reactions in the gas phase.(We regard that the TRS structure has the similar geometry as, or close to, the classical TS, except for the distance between the donor/acceptor carbons.) 36,38,52,54The most populated TS structures of the reactions of isopropanol (structure A) and cyclohexanol (B and C) are shown in Figure 1.From these structures, we found that the 3,4,5-CH 2 −CH 2 −CH 2 − group in cyclohexanol do lead away from the 9-phenyl group of the PhXn moiety.Therefore, the difference of the ΔE a values between the reactions of these two alcohols reflect largely the difference of the vibrational effects of the R groups.Due to the large standard deviations in ΔE a values of the two reactions, however, the remote R group effect on ΔE a cannot be differentiated.
The ΔE a for the reaction of 4-heptanol (entry 11) is the smallest among the System (3) reactions, but again the error is large so that its difference from that for the reaction of isopropanol may not give enough evidence to support the specific hypothesis in this paper.If this difference is real; however, it might be that the free rotation of the two large CH 3 CH 2 CH 2 − groups interact with the 9-phenyl group of the PhXn more often making the system more rigid and decreasing the ΔE a value as compared to that of the reaction of isopropanol.Interestingly, the observed activation entropy (ΔS ‡ ) of this reaction is the most negative value among the reactions of four alcohols, implicating that the system has a very tight reactive complex.Overall, the results from the System (3) reactions do not provide evident support for the specific hypothesis in this paper that relates remote heavy group vibrations to the ΔE a values.
The Remote ε-R Group Effects on ΔE a in System (4) Reactions.The System (4) reactions give us unexpected ΔE a results from changes of the R group in the acceptor of R−A + .It should be mentioned first that the ΔE a of the reaction of DMPBIH with MA + is much smaller than that of the reaction of HEH with the same (0.27 vs 0.95 kcal/mol in Table 1).We have found that the productive reactant complexes (PRCs) of the former reaction are tighter than those of the latter. 34That is possibly due to the fact that the DMPBIH is a 16.2 kcal/mol stronger hydride donor than the HEH so that the CT complexation is tighter in the former than the latter. 47Here, in the System (4) reactions using DMPBIH as a donor, when the size of the R group in the acceptors R−A + increases from methyl (for MA + ) to propyl (for PA + ) and hexyl (for HA + ), the KIE becomes almost T-independent (ΔE a from 0.27 to ∼ 0 kcal/mol, in Table 1) (also see Figures S1, S2).This significant decrease of the ΔE a value, rather than increase as expected, is possibly due to the steric interaction of the R group with the benzene ring fused with the 1,2-dihydroimidazoline ring of DMPBIH so that the system rigidity increases as the R size increases.We have reported the PRC structures of the reaction of DMPBIH with MA + and found that the most populated PRC structure has the CH 3 group in MA + being "stuck" in between the "fused benzene" ring and one N−CH 3 group of the DMPBIH (cf. Figure 2 of ref38).(This steric effect caused by the "remote" benzene structure of the DMPBIH is that the other donors in this work do not have.)It can thus be imagined that increase of the size of the R group would increase the rigidity of the system.Therefore, the significant decrease of the ΔE a due to the R change from methyl to the bulkier propyl or hexyl is likely resulted from the system rigidity increase due to the augmenting steric interactions between the donor and acceptor.One would indicate that the standard deviations in the ΔE a values are relatively large in these latter two systems so that the explanation may lack strong support, but that both systems have the same behaviors of almost T-independence of KIEs would suggest that the difference could be true (see Figures S1,S2).As far as the reaction of BA + is concerned, the ΔE a is the same as that of the reaction of MA + within the experiment error.We do not have a good explanation for this result but the benzyl group in BA + may also interact with the aromatic structures of the DMPBIH through π−π interaction altering the system rigidity.Nonetheless, we did not see the remote R vibrational effects on ΔE a in this series of reactions in a way to support the specific hypothesis in this work.
The Remote R Group Effects on k 2 .The remote heavy group effects on the rates (k 2 ) of the reactions refuse to be generalized among the four systems (Table 1).In System (1), k 2 (PAH) > k 2 (MAH) ∼ k 2 (BAH).In System (2), k 2 (BA + ) > k 2 (MA + ) ∼ k 2 (PA + ) ∼ k 2 (HA + ).The observed smallest enthalpy of activation of the corresponding reactions of PAH and BA + are mainly responsible for their fastest rates in the respective series of reactions (compare ΔH ‡ values in Table 1).This is the same for the observed fastest reaction of BA + with DMPBIH among the System (4) reactions.In the rest of the System (4) reactions, k 2 (MA + ) > k 2 (PA + ) ∼ k 2 (HA + ).The observed more negative entropies of activation (compare ΔS ‡ values in Table 1) for the reactions of PA + and HA + largely contribute to their slower rates.Lastly, in System (3), (4-HepOH).The observed slowest reaction of 4-HepOH is likely mainly resulted from the observed most negative ΔS ‡ value among the four reactions.

■ CONCLUSIONS
Our group is the first to systematically study the structural effect on the T-dependence of KIEs (represented by ΔE a values) for the hydride transfer reactions in solution.Our overall hypothesis on the basis of the enzymatic observations and explanations is that a more rigid system with densely populated short DADs in H-tunneling reactions gives rise to a smaller ΔE a value.While the rigidity(DAD)−ΔE a relationship has been studied in enzymes, in our research, we use the hydride tunneling reactions of NADH/NAD + coenzyme analogues to investigate the relationship in our hypothesis.Structural (electronic and steric) effects as well as solvent effects (including polarity and protic/aprotic considerations) on the ΔE a 's of the hydride transfer reactions have been studied.Results appear to be consistent with the enzymatic observations and support our hypothesis.
Another factor that can potentially affect the system rigidity is the structural vibrations.In this paper, we chose the remote heavy group vibrational effects to study.The remote groups chosen have the similar electronic effects and cause little steric effects so that the vibrational effects could be isolated to study.The remote groups are connected to the remote indirect reaction centers whose vibrations likely couple to the reaction center vibrations.The specif ic hypothesis of this paper is that slower vibrations of a heavier remote group increase the DAD sampling range and thus increase the ΔE a value.We designed the systems that contain such remote groups and determined the ΔE a 's in acetonitrile.We found that the remote heavy groups do not generally significantly increase the ΔE a 's in systems (1)−(3) where the steric effect appears not to be an issue.Importantly, none of these systems show that these groups decrease the ΔE a values as compared to the lightest methylated counterparts.This made us to infer that the remote heavy groups may have increased the ΔE a 's, i.e., consistent with the specific hypothesis.Therefore, even if the increases are so small that most of them fall within the experimental errors in these systems, we regard that it is worth to continue to investigate the remote group vibrational effect on the ΔE a 's for a large range of reactions or for other types of H-transfer reactions.
While our results appear not to provide strong support for the specific hypothesis we proposed in this paper, they, together with our previously published results from the structural and solvent effects study, suggest that the strength of the CT complexations due to the electronic properties of the donor and acceptor largely determine the system rigidities and ΔE a values.That is, the stronger CT complexations of more densely populated DADs, which are favored by stronger electron donors/acceptors, give rise to a smaller ΔE a value.In enzymes, study of the relationship uses different enzyme structures, rather than different substrate structures from our work; therefore, the DAD sampling difference is largely caused by the difference in protein vibrations.Nonetheless, the growing body of our results will be valuable addition to the current debates on the appropriateness of theories to describe hydride-as well as general H-tunneling reactions.They could also provide insight into the contentious role of protein dynamics in DAD sampling activation and enzyme catalysis.
Experimentally, the pseudo-first order rate constants (k pfo 's) were determined spectroscopically (by UV−vis) and the observed k 2 was calculated from dividing k pfo by the concentration of the large excess substrate (Sub) (for example, Sub-H or Sub-D), i.e., k 2 = k pfo /[Sub-H(D)].Then, Usually, the same concentrations of Sub-H and Sub-D solutions were used.
Six measurements of k pfo 's for the reactions of two isotopologues at different temperatures were made on the same day and repeated on other day(s).For a ΔE a determination, kinetics was determined over a temperature range of 40 °C, and the E aH and E aD were derived, respectively.A typical kinetic procedure at certain temperature is as follows.Six kinetic runs of 12 half-lives of the reaction were measured for each isotopic reaction back-to-back.The procedure was then repeated at other temperatures as quickly as possible (for example, 5, 15, 25, 35, and 45 °C, in order) so that the instrument settings were kept the same and the aging of the reaction solutions was the minimum (while the solutions were already stable, they were wrapped with aluminum foil and kept in refrigerator between temperatures to eliminate any possible error source.).Repetitions or kinetic measurements of the reactions of the same series of substituted substrates on different days sometimes used different batches of substrates and solvents and sometimes were done by different workers.That was to eliminate the effect of possible different impurity from unknown sources or human errors on the KIE measurements.Therefore, one KIE value was obtained from 18 repetitions.Pooled standard deviations were reported.Kinetic results (from the extent of reaction of close to 1% to 99.98% (corresponding to 12 half-lives)) were fitted very well/ excellently to the first-order rate law for k pfo derivation and to the Arrhenius correlations for E a derivation, both with R 2 = 0.9990−1.0000,many closer or sometimes even equal to 1.0000!Other details about the kinetic measurements as well as the raw data can be found from Tables S1−S5 and S10−S12 and the footnotes therein.
Kinetic Measurements of the System (3) Reactions.Kinetics of these reactions were determined differently from the above procedures.Same procedures in our publications for the study of the class of hydride-transfer reactions were followed. 33,56,58The k pfo was determined by following the decay of the PhXn + spectroscopically.The k 2 value was calculated from k pfo /[alcohol], and the KIE was calculated from the k 2 values (= k 2H /k 2D ).
80 μL of 0.1 M stock solution of PhXn + in acetonitrile was added to 8.0 mL of acetonitrile solution containing large excess of alcohol in a sealed 10 mL reaction vial that was preplaced in a water bath with a desired temperature.About 0.2 mL of the reaction aliquots were periodically taken into sample vials precooled in ice.The samples were immediately placed in a freezer (∼−20 °C) until 6 to 8 reaction aliquots within 1−3 half-lives of the reaction were collected.The aliquots were then analyzed by dilution of a preset volume in acetonitrile containing 3 M HClO 4 , and the corresponding UV−vis spectra at different reaction times, i.e., the kinetic scans, were obtained.Absorbance (Abs) decrease with time at 373 nm due to the PhXn + absorption was recorded.The obtained Abs-t data were fit to the first-order rate equation, -ln(Abs) = k pfo •t + constant, and the slope of the linear plot of −ln(Abs) vs t was taken as the k pfo of the reaction.The linear plots usually have regression coefficients (R 2 ) greater than 0.995.Each kinetic run was determined more than 2 times in most cases (see Tables S6−S9).Parallel determinations of the rates of the reactions involving normal and deuterated alcohols of same concentrations were used to derive the KIEs = (k 2H /k 2D = k pfo / k pfo ).Other details about the kinetic measurements as well as the raw data can be found from Tables S6−S9 and the footnotes therein.
Computations.All of the geometries in this work were optimized under the M06−2X 59 /Def2SVP 60 level of theory with a fine DFT integration grid in Gaussian 09 software.A scaling factor of 0.9687, which was fitted against the ZPVE15/ 10 database, 61 was applied in all of the free energy calculations in order to overcome the overestimate nature of the harmonic model.The free energy (ΔG°) of the hydride-transfer reaction from isopropanol to PhXn + to generate the protonated acetone and PhXnH in acetonitrile was calculated by using eq 7: °= °+ °°°+ (7)   G°s in the right side of the equation refer to the individual molecules of the reaction.The universal solvation model (SMD) was used.
The percentage (A i ) of the gas-phase TS structures of the reactions of isopropanol and cyclohexanol with PhXn + were calculated under the law of Boltzmann distribution of its free energy (G i ) by using eq 8: In this equation, N is the number of the TSs found, k B is the Boltzmann constant, and T is temperature.

Figure 1 .
Figure 1.Most populated gas-phase TS structures for the reactions of PhXn + with isopropanol (A, one of the three alcohols found, accounting for 94% of all) and cyclohexanol (B and C, two of the eight alcohols found, accounting for 83% of all).The space-filling structures in the background represent PhXn + , and the ball-and-stick structures in the foreground represent alcohols.The red atom is O.

Table 1 .
Structural Effects on the T-Dependence of Hydride KIEs of the Hydride-Transfer Reactions in Acetonitrile a a Numbers in paratheses are standard deviations.b Counterion: BF 4 − .c From ref35 d From ref34 e For 22 °C.